( QUANTITATIVE APTITUDE Simple Arithmetic Computations Profit and Loss Time and Work Percentages Problems on Numbers Ratio and Proportion Simple and Compound Interest Fascinating Fractions Test of Divisibility Averages Problems on Age Identities on Algebra and Simplification Logarithms Square Root Cube Root & Surds Rationalization of Surds Area Volume Trigonometry Geometry Statistics Probability Data Interpretation Miscellaneous ° ° ° ° ° ° oa ° ° ¢ ° ° ° ° ° ° ° a ° ° ° ° ° ° eotee10, every 2 001 0f3 ready Inthe collar every 3 owt ‘et A and B represent the sets of persons who can type tnd take shorthand respectively 8. The charges of hired car are € 4 per km forthe fst (0 km. €5 por km forthe next 60 km and 8 for eae ae ra Uae sca eae ce ‘ml mannose) oom See hntawihhinnay tn 3 cav0 e r=107 00 = 1800 s 9% Airs 8 sotto 's3 but Akl ony once a3 shoes = = ‘while A once in 2 shots When Bhs missed $7 tie a ‘les. has led wha the number be Then re 47 andthe lowest wore N30 tae 3B) 60 vied 0 72s Dy 00 ede aplanaton ‘Ans (A) 1a the total number of hots es. Then SSS wee ae‘The price at which an article e purchased i. ‘cast price abbreviated as CP Selling Price : The price at which an arc sold is called its sling rice abbreviated as $P ‘rotor Gain: TS. > CP tho sellers said to have a profit or gin. Prof = SPCR Lose: MS2.< CP, the seller is said whave incurred alss. | Loss = CPSP. Important Formulae : 2. Gains = Sain ,, 2 ose = os cr 4. tradesman allows two successive discount of 26 ‘and 10% It he ges € 108 for an atic, what wasren artiisdacrensed by 10%. To restore Sarton new price urbe inereased PY oe ee oe ae 25. 12 copies of Boks wore sold for © 1800 thereby (pining cont pce 03 copes. The core pice of =‘banana = €x and Cost goat Base axe yas 309100 7 13, Amachin is sold for € 5060 at» gai of 10%. What ‘AZua nave been te gn or lows percent if it had6 Ream do of work nS days. Bean aoe workin 9 days and Cean do 24 ofthat18. Acandoupiace of workin 12 day, whe B alone can oie in 15 doy, withthe help of they can finish ‘Aca doa work in 6 ys snd Bin 9 days. Mow many aye wil both tke together to complete the work? by Bass D) eo days‘han €) suffice for 95 men for 195 Sor mon = 08-20 0s: can do the workin de men ard 4 boys can the workin 5 be Nowe sosl 00x20 = 2020, 4 = id B can complete 2 work a 10 dys and 19 das ‘epectvely A sane art doing the work, Aer 3 ‘Zap le enn In how many Say wil te work Se comple? Whole wook ie compltedin 5 +3 = 8 das 441. and Btogeher can oa pec of workin 4S dar Band C together an do in 8 das and A Band © Sher ip At Cnc wt ih he 1m ocars DiemSURA'S © Quantitative Aptitude ‘Aas SURAS ¢ quanttatve Aptitode an do won 50 dos Ar 30 dora a enve the werk The whee wert way a Biplaneion | For the ret 10 days: Stn mete ita tes aot do a workin sataen days 18, 1 Sore women an fein 15 aps. Wht , ‘ans:ta) | the ro Between the copcty of = man and 8 tthe = ays, and B tte y dys to compte No of days remaining = 350 200 = 150 _ NoclDays Kmeag — NoetMin‘Atarge watecsnalon weigh 20k with 98 % of ‘Sei ing water es sllowed vo tad in thes (6 atu + 4 carn) dy wo = SS Sandman 7 More is done by them in dy +2 wer ona yh ep en an fila nice of wrk 15 ap fimo ean 80 men de the ame work) venteaptanaion = ato of men and women = 1000: 1075 = 40. Number of men in he ttl popu = $2880 100 w 2822 915, isons 100-7 20555 af boys and 40% of gir led. The percentage ‘ot candidates the posted war ‘00%. 208 then gg) 20% By what percent shoud thence? Dereddced rw Ge ack the oie2-88 109 = 24100 =: aa «100 = 26100 30%z a ‘Ans @) questions in 8 paper, the given number by 119, let K bo the | 12 Out of five n se >) 60 Explanation = ‘Ane ) ‘et the eiginal umber of parsons be= = ‘Share of ech persons = 2800, 1 the no, of persons be increased by 15, then the new share ofeach personthe rnainder stained by maberacting# numba "cco squar 8 times the umber: hatplanation _ Ue the number of 20 pase coins = x ‘and 25 pase coins = y Given. r+ = 50 ‘or + 26) =1128 SoWving x= 25, = 25 39. The aiference berween 120 percent of « number ‘and ts three-fourt o 50% ofthat number Whats ‘hat number? 40. A.cwo digit numbers 6 toes the sum of is igs. ‘When the sum oft digits added to the manor | 12 ‘he revuli 63. What ir tha mame? 5 a ee na fothat Rist son et ne80 + comin ote a See pe apd in ops rs Haine oa: . seg so rempectiv tran are hs Dee esse tes arenes cred 2” er ctnew un are newb ‘Beplanation: oe) ie ieee eetete ‘Appu be 2 and 3 Feng ot ces mech hee peers A Ba Mea acre tral et Set ons tae te eteflim nts aoa sa 7h Woes geet 1200, inten rien Bezspeed of thre cars are in the rtio 2: 1:2. The {tio betwen the ie taken by thet travel the ‘Some distance ? planation: Let the corto each banana be & and he pple be &. the mixture is replaced by the same amount of ater: Pind the rate of mil to weter inthe ne smieeure” was ms:4 ont D233 Eeplanaton:SURR'S + Quantitative Aptitude SIMPLE AND COMPOUND INTEREST 3]"12, The compound interest on 4 certain sum of money {25% fr 2 yeas in € 328, The spl intron of ‘hat rum ac te w t3z2WAono = SS iciernotcome ies Sots See gene arene | ‘whch tnt i ce gic 427. Th population of wey decreases by 3% af {nti se begining of eery yer the io, ‘The population is decreasing, hence ~ signi replaced | ie ermaloe o : |& Wich ofthe fllowing ete smallest perfec square, ‘exactly divisible by 8.15 and 247 A) 2500 3) 3600 ©) 1600 ) 900 Explanation: thas ‘The LCM of 8, 15 and 24 is 120. Now the ‘number would bein multiple of 120, which needs Perfect square ao © Required number = 3600 8. What is the diference ecween the LCM and H.CF ‘ofthe numbers 60,75 and 907, 2) |, Tho LGM of €0, 75 and 90 is 900 | The H.CF of 60,75 and 9015 15 _ Required dtference = 900-15 = 887 ‘how many stodent 17 BF trnogar canbe equal diviegy” Ba. x" ‘ans: () Lema 10, 12,15 = 120: “To ind the largest our digit number whichis» multiple equeed number = 0999 ~39 = 9960 40, A.number ying between 1000 and 2000s such that ‘cuaivision by 2.3.4 5,6, 7.8 leaves remainders 3123.4, 5, 6 and 7 respectively. The mimber is wiste 1778 ‘explanation LeMor2345.6.7.81s840 10% seconds and 18% seconds respectively. After s a‘then (9) 324 and 264 are divisible by 4 15324 ~ 264:= 60 i also divisile by 4, PROBLEMS FOR 1. Which digit should come inthe place of and 3 Hf ‘the number 62684 © ie diviibe by both 8 and 9? aso © Sando, [Bxplanation: ‘Ans. (8) ‘The number formed by the last two digits inthe given ‘number 67020594 isnot divisible by 8SURKS © quantitative Aptitude meen ‘ty 4-2 and e+ oe an | 20. A mumber 470+ 0s vii by beth 3 ‘he non-sra disin tha hundredth end enh place om B75Expinacon: ‘Toa oge of brothers = 12 X 4'= 48 years els ‘Piwew average when mothers age sincuded = 12+ 5 | * = iryeare i 23, ‘The average age of 8 men is increased by 2 years ‘when two of them whose ages are 21 and 23 years {Sefer bye ew mon. The weg oe of Azayers —B) 22years ©) 36 yours Dy 30 years : planation: ‘Ans: (0) | 5 ‘Overall increase inthe total age = 8 x 2 = 16 years ‘Sum of ages of two new men = 21423416 = 60 years ‘Average age of them = 52 = 20 yours‘The average age ofthe mother and her 8 childrens 2 yeas, whichis reduced by 5 years ifthe age of ‘he mothers excluded. How os the mothary '8) 40 yeorsSURKS + cunttative Atte wtatreaptnwde 17 Ran oe lil wes ba war 0 aA which ae hin og wi 2 ines ha eesot his answer was By how oy how mach (oe) beth‘Oaixo2ixo21+0021x0.021x0.021 ‘0.62 0.63 0.53+0.063 0 063%0.009an: of two guantes is legume the sur of tet urns en separiomx= 2 00 y= (2% = 2, (2b) = then 9 (a) 18 alogim = logs, then the value of = no B30 Explanation: ans 1og400og5+ og 8+ 12) =o 322 20 tg =1 og, a! -1)-1og,(0419=3. nd ee vat a, me De(8. Find the square roe of 27225, ‘156 coor3 Find he ube ror of 1728, ; @ Quantitative Aptitude 2 WT = 87-56 ©. What is the smallest number by which $2728 must bbe divided so thatthe quotients cube?"‘Beplanation; ana) ‘Area of rectangular frame = 54 x 64 = 3450 sqm Required no, of stickers = $88 122 23. A circular garden of radius 42 metres Is to be ‘Surrounded by aroed 42 metres wide. Whats the | 25, Inthe figure drawn below, what isthe | Percentage of the dotted portion of are au compared tothe toca rea? Fee TET1 ; Sees « cuannnre genie aa oe ior eeee = 812m een BE ct xn am 16. Three equal cubor are placed adjacent in row ‘ind the ti fetal surtace aren ofthe new cuboid {that of th rum of Uh surface areas of the three wre wo:7 UMS + uantntive Ape radius and slant height of « T tame of terion cf SPO Trai te crved race nary le eral. a = 2dbebnend 5 Saget et 30) = 2008) = 14 Sela raised? W056 m ® 032m ©) 023m D) 047m wees macs O12 Det Explanation: ‘Volum of cylinder =x, "h, = x7° 10 = 490 xem Volume of 2nd cylinder = m,"n, = #720. 080mm? aon 1 OE Lays att 18, How many cubic metres of earth must be dugout to sink a well 22.5m deep and diameter 7m? ‘§) 800m ) Bas me ©) 866.25 m? D) 832.5 mtanAtun Seana + 5) = SOAtan man (acn) = weAsman vitaeSuRwS © cwontutie tebe"An angle whove measure is exacy equa 10 90"is called an at angie ‘Obtase anglepet pi afanse: ee ‘et {and m be two paral lines, n bea tranevrsat tarp ‘Verily opposite angles: Two ngs formed by te say Spent nr tne ure (AS). EO) Tey ar erica opposte anges. erent oppose Sojesarabwos eau. Inrior angle’ Ares which ar whi tbe paral ines im ere called interior angles. In th figure, C, D.E. Fare terre Exterior angles Angles whi ar not within the paral Tne art eed entation nthe gue, A.B. H. peneror glee Corresponding angles:(A.2, (0, (0.30, (60) ar called ‘Seatang kage Twe pl fangs rool ‘Aternate interior angles: (CE (0.7 are aterateitrcr ‘cic Toes pa ofertas iar safes re equ ‘Complementary angles: ede sum o two angles is 90" then the pa of ve cha umatem antes 9 ent par angles the ‘pales este eelieciele 1007 tien angles are sid tobe aupplomentary angles,“> P PROBLEMS FOR PRACTICE 1 The the angle TF aa a - oor De ‘Bepleatins ‘ Complement of 72°= 00" ~ 72" = 18° oars aoe Satelite eer ee Pe. ee(© Angle subtended by an are of the circle is = 2 rae ernest ca aan? BY 70" soaeeees © Explanation: ‘ans (€) _ZAPR = 90° (Ange ina semicircle ea right angle) | 2eA8 + ZarB + ZAP = 160" (um of angles ofa triangle) =: PAB = 180" ~90"= 42" = 48° But 2PaB = 208 (Angles in the same segment ofa ice are equal) 2208 = 48" 14, In the figure, 0 is the centre ofthe cele 1 = 160" find he vale of 2¢ +p Wy 5,280" double the angle subtended bythe are on the | x70'| is the = 2000 | = Fetieee_gunass ¢ quantitative APIS ee theorem, AC — ~ 4 3 oo Ae e200" = AC 30/2 ae a Fon th Ora) Be cer.s1e-s001.0 ‘AB Vertical tick _ AD _6_2 “Taking postive square root AD = 8 a2 25. ABCD is square. Fis the midpoint of AB. BE is one {ir of BC: If the area of th triangle FRE is 108 Seem Rnd the length of AC approval 50 em 3B) stem seem sem ‘Explanation: a Let these ofeach square be em, A, ‘ns: (@) ‘more rmiar daeeines ke 5Diectons (Qn. 11010): Read the oling ale andar te uesons based on ‘Expenditure on various department of a University during 1995 and 2000 © crores)be ieee ater mooreSeed cmpoent par aie Se eran toting | 3 Toten rin lanower the questions. aaa ‘Sten Popuiaton a Metopons : 1991 Qe 42. Bangalore population of Hyderabad. Soot Bt & Peplnion ot Dah wae, a oe =F oe = ee or — 7a oe cS Sas mcey Pate | ee ee on 35 _ = SS xo19tatn= 32.165 en = 22es 1 SURA'S © quanitative Aptitude Towne wat Qe mon ioporant good grain the ;eplanation: ‘Ans: 0) Increace intl production ofl types of cars rom 1991 wise = 0-1877, tmwhich year was the profi ara percentage of F085cece lt MR an gn eee tans | | ee Bact | second a= ( SURAS + Cuantkatve Aptitude oD airy 24. Divide 169 in the ratio 2:5 : 6. The rupees in Mumber of gs = 200-80 = 120 ae idee we iiee‘30, 18 men ull ship model in 7 days. How many days 3 eatd take for 13 men to build the same model? er B85 Ss RS eeeLet the edge ofa cube be x cm. <: Length of cuboid = em. ‘width = em, Hight = em, 5 tal surface area = 2 Ux b+ bx n+n xD 3 2Ge +24 3r) = 350 350 a70 = 275 a¥= "Baas wre VBa5en 36. °8 began busines wit € 450 and wat sherds by i300, Boned a ‘eth pote wars vided ite tmnt {Se ond ete your The vue at ae ms si Ds epanaion: 2S"ace af the same time. Find the lange a he ‘300 meee 3 270 metre, ©) 360 mewe Explanation:Dircns (Qne 115-117 + Say the fling -nformaton cael on one a usn genBln Tor 0 Sets Sak‘na company 10 empoyoos got a salary of 26,200 Sidhu! ts tployne econ of 23,550 00h, ‘he nveraye salary ofthe emplorees in the